Barotropic elliptical dipoles in a rotating fluid

Barotropic f-plane dipolar vortices were generated in a rotating fluid and a comparison was made with the so-called supersmooth f-plane solution which—in contrast to the classical Lamb–Chaplygin solution—is marked by an elliptical separatrix and a doubly continuously differentiable vorticity field. Dye-visualization and high-resolution particle-tracking techniques revealed that the observed dipole characteristics (separatrix aspect ratio, cross-sectional vorticity distribution and vorticity versus streamfunction relationship) are in close agreement with those of the supersmooth f-plane solution for the entire lifespan of the dipolar vortex.     

A solution to the hydraulic fracture problem in the traveling wave form

Solutions to the system of equations describing the propagation of hydraulic fracture cracks in a porous medium are obtained in the traveling wave form. The only sought solution is the separatrix of integral curves on the “penetration depth-crack width” plane. Some necessary dependencies that should be given at the crack inlet are found for the fluid flow rate and the fluid pressure. The crack width and the fluid penetration depth are related by power laws in the limiting cases when the crack propagation processes or the fluid penetration processes are dominant.     

Thermal convection in a nonequilibrium turbulent medium with rotation

The equations of thermal convection in a rotating plane horizontal layer of nonequilibrium turbulent fluid are obtained, the system of equations is linearized and the boundary value problem is formulated. Some general properties of the perturbation spectrum are found and a solution, which includes the classical solution in the absence of turbulence as a limiting case, is obtained.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 62–70, November–December, 1994.     

Break-Up of Aerosol Agglomerates in Highly Turbulent Gas Flow

Agglomerate aerosols in a turbulent flow may be subjected to very high turbulent shear rates which through the generation of lift and drag can overcome the adhesive forces binding the constituents of an agglomerate together and cause it to break-up. This paper presents an analysis of the experimental measurements of the breakup of agglomerates between 0.1?C10???m in size, in a turbulent pipe flow followed by an expansion zone with a Reynolds numbers in the range 10⁵ to 10⁷. The analysis shows that even in wall bounded turbulence, the high turbulent shear stresses associated with the small scales of turbulence in the core can be the main source of breakup preceding any break-up that may occur by impaction at the wall. More importantly from these results, a computationally fast and efficient solution is obtained for the General Dynamic Equation (GDE) for agglomerate transport and breakup in highly turbulent flow. Furthermore the solution for the evolution of the aerosol size distribution is consistent with the experimental results. In the turbulent pipe flow section, the agglomerates are exposed continuously to turbulent shear stresses and experience more longer term breakup than in the expansion zone (following the pipe flow) where the exposure time is much less and break-up occurs instantaneously under the action of very high local turbulent shear stresses. The validity of certain approximations made in the model is considered. In particular, the inertia of the agglomerates characterised by a Stokes Number from 0.001 for the smallest particles up to 10 for 10???m particles and the fluctuations of the turbulent shear stresses are important physical phenomena which are not accounted for in the model.     

Vortex Scattering of Monatomic Gas Along Plane Curves

An invariant submodel of gas dynamics equations constructed on a three-dimensional subalgebra with a projective operator for the case of monatomic gas is under consideration. The submodel is reduced to an Abel equation, with integral curves constructed for it. For a separatrix of a saddle, an approximate solution is studied. Such solutions describe the vortex scattering of gas along plane curves placed on the surface of revolution.     

Persistent Non-Homogeneous Features in Periodic Channel-Flow Simulations

Time-resolved simulations of simple shear flows, such as boundary layers and channel flows, are often used as precursor simulations that provide the inflow-boundary conditions for simulations of turbulent flows in and around more complex geometries. For both the precursor and main simulations, the accuracy of the calculated mean flow relies on the simulations being run for long enough to contain the full spectrum of turbulent processes, resulting in a physically valid statistical representation. The time scale needed to achieve convergence of statistics from fundamental studies of simple shear flows is based on data that is averaged in spatial directions in which the flow geometry is invariant—i.e. directions in which homogeneity is expected to be the limiting case. This paper reports and discusses features that represent significant departures from spatial homogeneity of the flow in such a direction, that persist on this time scale, thereby limiting the spatial uniformity of a simulated turbulent inflow. The persistence and size of the features is quantified. A range of simulations for different combinations of domain dimensions and flow parameters has been performed with two independent codes (DNS and LES) to explore how the persistence and size are controlled. While no definitive physical mechanism has been identified, it is suggested that the features may be related to experimental observations of persistent structures in wall-bounded flows.     

Two-layer turbulent flow over a rough rotating surface

A model of turbulent incompressible fluid flow over a rough surface under the action of the Coriolis force with a turbulent transfer coefficient corresponding to the Prandtl mixing length is proposed. A solution of the problem, asymptotic in the small Coriolis parameter, is presented for horizontally uniform steady-state flow. It is shown that for a small Coriolis parameter the velocity profile and the turbulent transfer coefficient can differ substantially from the limiting expressions known from Prandtl theory. The smaller the roughness coefficient, the greater the difference.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 61–67, July–August, 1995.     

暖季强降雨对多年冻土南界斜坡路基稳定性影响分析

为阐明表面活性剂水溶液的减阻作用,使用LDV对零压梯度的二维湍流平板边界层中的CTAB 表面活性剂水溶液的湍流特性进行了实验研究. 结果表明：与牛顿流体相比,CTAB水溶液边 界层的粘性底层增厚;主流时均速度分布有被层流化的趋势,对数分布域上移;主流方向速 度湍动强度峰值减小,且远离壁面,在靠近边界层中部,出现第2峰值;垂直于主流方向的 速度湍动强度受到了大幅度抑制,雷诺应力沿着边界层厚度方向几乎为零. 结果说明CTAB 水溶液具有减弱湍流湍动各个成分相关度的作用,从而能够使雷诺应力降低、湍流能量生成 项减小最终降低流体的输送动力.     

On the motion of particles in turbulent duct flows

Existing knowledge on particle deposition rates on walls from turbulent pipe and channel flows is summarized and it is shown that discrepancies exist between experimental and theoretical findings. To contribute to the existing experimental information, laser Doppler measurements are reported of the flow field of a glass particle-air two-phase flow. The results reveal certain seemingly peculiar behaviors of the particles which obviously defy the predictions of the conventional analyses of turbulent two-phase suspension flows.In an accompanying approximate, yet pragmatic theoretical approach, an attempt is made to find a rational basis for the explanation of these experimentally observed particle behaviors. It is shown for the particles in the present study, there exists a limiting size above which their response to the agitation of the fluctuating motion of the surrounding fluid could be treated as if the flow were laminar. On this rational basis, these experimentally observed particle behaviors can then be qualitatively explained by the existing theory of particle excursion in a laminar shear flow field.Reported also is a suggestion to extend the present analysis to a dispersion of particles of multiple sizes.     

Heat and mass transport in nonisothermal turbulent flow when there is a screen formed by a gas of a different nature

We obtain a limiting relative law for heat and mass transport when there is a gas screen in a turbulent boundary layer, which makes it possible to take into account the effect of nonisothermal flow on the turbulent heat and mass transport beyond the region where the foreign gas is injected. The theoretical results are compared with experimental data on the intensity of burn-up of a graphite surface in an air flow when helium is injected through a tangential slit. The experimental data were obtained from the diffusion region of the burn-up.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 152–156, September–October, 1971.     

On the stability of generalized hill''s equation with three independent parameters

This paper presents a stability criterion of a generalized Hill's equation with three independent parameters, examined by means of an asymptotic method. The theory has been applied to a special form of Hill's equation and the region of stability, has been graphically illustrated. The separatrix between bounded and unbounded solutions yields in parametric space the contour of a ‘stabilitatskörper’ in which the solution is always stable.     

Non-linear argumental oscillators: Stability criterion and approximate implicit analytic solution

The behaviour of a space-modulated, so-called “argumental” oscillator, is studied. The oscillator is submitted to an external harmonic force, which is amplitude-modulated by the oscillator's position in space. An analytic expression of a stability criterion is given. Using the averaging method, an integrating factor and a Van der Pol representation in the (amplitude, phase)-space, an exact implicit analytic solution is given when there is no damping, and an approximate implicit analytic solution is given when there is damping, allowing the plotting of the separatrix curve. An attractor is identified.     

Asymptotic analysis of turbulent boundary layer flow on a flat plate at high Reynolds numbers

The equations of the turbulent boundary layer contain a small parameter — the reciprocal of the Reynolds number, which makes it possible to carry out an asymptotic analysis of the solutions with respect to that small parameter. Such analyses have been the subject of a number of studies [1–5]. In [2, 5] for closing the momentum equation algebraic Prandtl and turbulent viscosity models were used. In [1, 3, 4] the structure of the boundary layer was analyzed in general form without formulating specific closing hypothesis but under additional assumptions concerning the nature of the asymptotic behavior of the limiting solutions in the various regions.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 106–117, May-June, 1993.     

High-order strand grid methods for shock turbulence interaction

ABSTRACT

In this work, we examine the flux correction method for three-dimensional transonic turbulent flows on strand grids. Building upon previous work, we treat flux derivatives along strands with high-order summation-by-parts operators and penalty-based boundary conditions. A finite-volume like limiting strategy is implemented in the flux correction algorithm in order to sharply capture shocks. To achieve turbulence closure in the Reynolds-Averaged Navier–Stokes equations, a robust version of the Spalart–Allmaras turbulence model is employed that accommodates negative values of the turbulence working variable. Validation studies are considered which demonstrate the flux correction method achieves a high degree of accuracy for turbulent shock interaction flows.     

The turbulent boundary layer of dissociated gas in the initial section of a tube

Many theoretical and experimental papers [1–4] have been devoted to investigating the turbulent boundary layer in the initial section of a channel. For the most part, however, the flow of an incompressible fluid with constant parameters is considered. There are many practical cases in which it is of interest to treat the development of the turbulent boundary layer of gas in the initial section of a pipe when conditions are strongly nonisothermal. A solution of a problem of this type, based on the theory of limit laws, is given in paper [1]. The present article extends this solution to the case of the flow of a high-enthalpy gas when the effect of gas dissociation on the turbulent boundary layer characteristics must be taken into account. We shall consider the flow of a mixture of i gases which is in a frozen state inside the boundary layer, and in an equilibrium state on its boundaries. Formulas are derived for the laws of friction and heat exchange, and a solution is given for the turbulent boundary layer equations in the initial section of the pipe when the wall temperature is constant and the gas flows at a subsonic velocity.Finally the authors are grateful to S. S. Kutateladze for discussing the paper.     

A Collocation-Based Algorithm for Computing the Pull-In Range of a Class of Phase-Locked Loops

The pull-in range (ω_p) of a phase-locked loop (PLL) is defined as the maximum value of loop detuning ω_0s for which pull-in occurs from anywhere on the PLL's phase plane. That is, pull-in is guaranteed from anywhere on the phase plane if ω_0s < ω_p. Simple approximation is available for computing ω_p for the high gain PLL where saddle-node bifurcation occurs at ω_0s = ω_p. Unlike the high gain case, a simple approximation for ω_p is not available for the low gain case where bifurcation from a separatrix cycle occurs at ω_0s = ω_p. The vector field model for a class of second-order PLLs is shown to have rotational properties, which imply the existence of a separatrix cycle. The external stability of this separatrix cycle is an indicator of the type of bifurcation (saddle-node or separatrix cycle) which terminates the limit cycle associated with the PLL's stable false lock state and the PLL pulls-in (i.e. achieve phase lock). A formula is given for determining the separatrix cycle's stability, which indicates that these paratrix cycle is externally stable for small values of closed loop gain. A collocation-based algorithm is presented for computing the PLL's separatrix cycle and the value of pull-in range frequency ω_0s = ω_p at which a stable separatrix cycle exists.     

Propagation of a laminar jet of electrically conducting fluid in a uniform magnetic field

Several papers [1–4] have considered the propagation of a plane laminar jet of incompressible conducting fluid in a uniform magnetic field for magnetic Reynolds numbers much less than unity. These papers have investigated the flow of a free jet in a transverse magnetic field for small values of the magnetic interaction parameter. Equations for the first approximations were obtained in [1, 2] by a series expansion in the small interaction parameter close to the ordinary solution (without magnetic field) for the jet. The equations for the zero-th and first approximations were integrated in [3]. The same author also found a similar solution for a turbulent jet, the turbulent transfer coefficient being chosen according to Prandtl's method. As regards the solution found in [4], it suffers from the defect that the constant of integration which connects the real velocity profiles with those found in the paper remains undetermined. The present paper gives an approximate solution of the same dynamic problem of the propagation of a free plane jet in a uniform field, no assumption being made as to the smallness of the interaction parameter. In order to do this the integral method of solution, common in ordinary hydrodynamics [5, 6] is employed. The solution of the problem is generalized to include the case of a finite value of the Hall parameter.     

Drop evaporation in a turbulent gas jet

Evaporation of a semidispersive drop system in a turbulent gas jet is considered. A method for calculating drop evaporation in a turbulent gas jet is proposed based on a simplified solution of the scattering problem for an evaporating admixture. Evaporation of water as it is atomized in a turbulent air jet is experimentally studied. Approximate agreement is obtained between the results of the calculations and experiments.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 73–79, January–February 1976.     

矩形槽道内表面活性剂减阻流体场特性

采用粒子图像测速仪对矩形槽道内表面活性减阻流体在流动方向(x方向)与壁 面垂直方向(y方向)所在平面的流场进行了测量,分析了速度、涡量、速度脉 动相关量在流场内的瞬态分布,以及对500幅相同工况的流场进行了统计平均. 结 果显示: 与牛顿流体相比, 表面活性剂减阻流体接近于层流流动,横向速度脉动被大幅 减弱,导致湍流输运减弱,雷诺应力远远小于水. 减阻流体流向速度脉动呈条带 特征,沿流动方向发展,反映了减阻流体不同于水的湍流输运特征.